Automaton Homework Help

1.Show that if we apply the subset construction to a deterministic automaton, we either get the same automaton, with each state s renamed {s}, or we add a dead state (corresponding to the empty set of states).

2.Some automaton have state-input combinations for which there is no transition at all. If state s has no transition on symbol x, we can add a transition from s to a special “dead state” on input x. The dead state is not accepting, and has a transition to itself on every input symbol. Show that adding a “dead state” produces an automaton equivalent to the one with which we started.

3.We can represent an automaton by a relation with attributes State, Input, and Next. The intent is that if (s, x, t) is a tuple, then input symbol x is a label of the transition from state s to state t. If the automaton is deterministic, what is a suitable key for the relation? What if the automaton is non deterministic?

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4.Design an automaton that reads a word (character string) and tells whether the letters of the word are in sorted order. For example, adept and chilly have their letters in sorted order; baby does not, because an a follows the first b. The word must be terminated by a blank, so that the automaton will know when it has read all the characters. ( we must not accept until we have seen all the characters, that is, until we reach the blank at the end of the word.) How many states do you need? What are their intuitive meanings? How many transitions are there out of each state? How many accepting states are there?